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Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps

· 2022 · math.DG · arXiv 2203.15681

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abstract

Let $\mathcal{M}_{g,n(g)}$ be the moduli space of hyperbolic surfaces of genus $g$ with $n(g)$ punctures endowed with the Weil-Petersson metric. In this paper we study the asymptotic behavior of the Cheeger constants and spectral gaps of random hyperbolic surfaces in $\mathcal{M}_{g,n(g)}$, when $n(g)$ grows slower than $g$ as $g\to \infty$.

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math.DG 1

years

2025 1

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CONDITIONAL 1

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Spectral gaps on thick part of moduli spaces

math.DG · 2025-01-16 · conditional · novelty 7.0

For every fixed k and every ε>0, the maximum of λ_k - λ_{k-1} over genus-g hyperbolic surfaces with systole at least ε tends to 1/4 as g→∞.

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  • Spectral gaps on thick part of moduli spaces math.DG · 2025-01-16 · conditional · none · ref 42 · internal anchor

    For every fixed k and every ε>0, the maximum of λ_k - λ_{k-1} over genus-g hyperbolic surfaces with systole at least ε tends to 1/4 as g→∞.